Memoirs of the American Mathematical Society 2014; 110 pp; softcover Volume: 231 ISBN10: 147040981X ISBN13: 9781470409814 List Price: US$71 Individual Members: US$42.60 Institutional Members: US$56.80 Order Code: MEMO/231/1084
 The structure space \(\mathcal{S}(M)\) of a closed topological \(m\)manifold \(M\) classifies bundles whose fibers are closed \(m\)manifolds equipped with a homotopy equivalence to \(M\). The authors construct a highly connected map from \(\mathcal{S}(M)\) to a concoction of algebraic \(L\)theory and algebraic \(K\)theory spaces associated with \(M\). The construction refines the wellknown surgery theoretic analysis of the block structure space of \(M\) in terms of \(L\)theory. Table of Contents  Introduction
 Outline of proof
 Visible \(L\)theory revisited
 The hyperquadratic \(L\)theory of a point
 Excision and restriction in controlled \(L\)theory
 Control and visible \(L\)theory
 Control, stabilization and change of decoration
 Spherical fibrations and twisted duality
 Homotopy invariant characteristics and signatures
 Excisive characteristics and signatures
 Algebraic approximations to structure spaces: Setup
 Algebraic approximations to structure spaces: Constructions
 Algebraic models for structure spaces: Proofs
 Appendix A. Homeomorphism groups of some stratified spaces
 Appendix B. Controlled homeomorphism groups
 Appendix C. \(K\)theory of pairs and diagrams
 Appendix D. Corrections and elaborations
 Bibliography
